Combined Noise and Clock CRLB Error Model for the Optimization of Node Location in Time Positioning Systems

The emergence of autonomous vehicles with high needs for accuracy in location has hardened the requirements of the positioning systems used for navigation. Local Positioning Systems (LPS) have shown an excellent adaptation to these conditions, thanks to stability and reduction in the levels of positioning uncertainty. The accuracy achieved by methodologies based on temporal measurements depends mainly on the uncertainties in the measurements of these systems. In this aspect, the presence of noise and the existence of temporary instabilities in measurement clocks, depending on the distribution of sensors in the environment, acquire great relevance. In this article, we introduce for the first time in the authors' best knowledge a Cramér-Rao Lower Bound (CRLB) model for the quantification of the global uncertainty in positioning systems caused by both noise and temporary instabilities in the measurement devices. Additionally, this technique is applied to the optimization of sensor distributions for Time of Arrival (TOA), Time Difference of Arrival (TDOA) and Asynchronous TDOA (A-TDOA) architectures using a Genetic Algorithm in a non-uniform 3D environment. Results show that A-TDOA methodology significantly overcomes synchronous architectures in terms of global accuracy and stability when noise and clock errors are considered in time measurements of LPS applications.